First confirm that is a solution to the ODE,
We have
Substituting into the ODE gives
Suppose is another solution to this ODE. Then
and substituting these into the ODE yields
Let . Then the remaining ODE is linear in :
Multiply both sides by the integrating factor, , and condense the left hand side as a derivative of a product:
Integrate both sides with respect to and solve for :
Back-substitute and integrate both sides with respect to to solve for :
Back-substitute again to solve for :
already captures the solution , so the remaining one is